LECTURES
ON STELLAR STATISTICS

BY

C. V. L. CHARLIER

SCIENTIA PUBLISHER
LUND 1921

HAMBURG 1921
PRINTED BY LÜTCKE & WULFF

CHAPTER I.

APPARENT ATTRIBUTES OF THE STARS.

1.

Our knowledge of the stars is based on their apparent attributes, obtained from the astronomical observations. The object of astronomy is to deduce herefrom the real or absolute attributes of the stars, which are their position in space, their movement, and their physical nature.

The apparent attributes of the stars are studied by the aid of their radiation. The characteristics of this radiation may be described in different ways, according as the nature of the light is defined. (Undulatory theory, Emission theory.)

From the statistical point of view it will be convenient to consider the radiation as consisting of an emanation of small particles from the radiating body (the star). These particles are characterized by certain attributes, which may differ in degree from one particle to another. These attributes may be, for instance, the diameter and form of the particles, their mode of rotation, &c. By these attributes the optical and electrical properties of the radiation are to be explained. I shall not here attempt any such explanation, but shall confine myself to the property which the particles have of possessing a different mode of deviating from the rectilinear path as they pass from one medium to another. This deviation depends in some way on one or more attributes of the particles. Let us suppose that it depends on a single attribute, which, with a terminology derived from the undulatory theory of Huyghens, may be called the wave-length (λ) of the particle.

The statistical characteristics of the radiation are then in the first place:—

(1) the total number of particles or the intensity of the radiation;

(2) the mean wave-length (λ₀) of the radiation, also called (or nearly identical with) the effective wave-length or the colour;

(3) the dispersion of the wave-length. This characteristic of the radiation may be determined from the spectrum, which also gives the variation of the radiation with λ, and hence may also determine the mean wave-length of the radiation.

Moreover we may find from the radiation of a star its apparent place on the sky.

The intensity, the mean wave-length, and the dispersion of the wave-length are in a simple manner connected with the temperature (T) of the star. According to the radiation laws of Stephan and Wien we find, indeed (compare L. M. 41[1]) that the intensity is proportional to the fourth power of T, whereas the mean wave-length and the dispersion of the wave-length are both inversely proportional to T. It follows that with increasing temperature the mean wave-length diminishes—the colour changing into violet—and simultaneously the dispersion of the wave-length and also even the total length of the spectrum are reduced (decrease).

2.

The apparent position of a star is generally denoted by its right ascension (α) and its declination (δ). Taking into account the apparent distribution of the stars in space, it is, however, more practical to characterize the position of a star by its galactic longitude (l) and its galactic latitude (b). Before defining these coordinates, which will be generally used in the following pages, it should be pointed out that we shall also generally give the coordinates α and δ of the stars in a particular manner. We shall therefore use an abridged notation, so that if for instance α = 17^h 44^m.7 and δ = +35°.84, we shall write

(αδ) = (174435).

If δ is negative, for instance δ = -35°.84, we write

(αδ) = (174435),

so that the last two figures are in italics.

This notation has been introduced by Pickering for variable stars and is used by him everywhere in the Annals of the Harvard Observatory, but it is also well suited to all stars. This notation gives, simultaneously, the characteristic numero of the stars. It is true that two or more stars may in this manner obtain the same characteristic numero. They are, however, easily distinguishable from each other through other attributes.

The galactic coordinates l and b are referred to the Milky Way (the Galaxy) as plane of reference. The pole of the Milky Way has according to Houzeau and Gould the position (αδ) = (124527). From the distribution of the stars of the spectral type B I have in L. M. II, 14[2] found a somewhat different position. But having ascertained later that the real position of the galactic plane requires a greater number of stars for an accurate determination of its value, I have preferred to employ the position used by Pickering in the Harvard catalogues, namely (αδ) = (124028), or

α = 12^h 40^m = 190°, δ = +28°,

which position is now exclusively used in the stellar statistical investigations at the Observatory of Lund and is also used in these lectures.

The galactic longitude (l) is reckoned from the ascending node of the Milky Way on the equator, which is situated in the constellation Aquila. The galactic latitude (b) gives the angular distance of the star from the Galaxy. On plate I, at the end of these lectures, will be found a fairly detailed diagram from which the conversion of α and δ of a star into l and b may be easily performed. All stars having an apparent magnitude brighter than 4^m are directly drawn.

Instead of giving the galactic longitude and latitude of a star we may content ourselves with giving the galactic square in which the star is situated. For this purpose we assume the sky to be divided into 48 squares, all having the same surface. Two of these squares lie at the northern pole of the Galaxy and are designated GA₁ and GA₂. Twelve lie north of the galactic plane, between 0° and 30° galactic latitude, and are designated GC₁, GC₂, ..., GC₁₂. The corresponding squares south of the galactic equator (the plane of the Galaxy) are called GD₁, GD₂, ..., GD₁₂. The two polar squares at the south pole are called GF₁ and GF₂. Finally we have 10 B-squares, between the A- and C-squares and 10 corresponding E-squares in the southern hemisphere.

The distribution of the squares in the heavens is here graphically represented in the projection of Flamsteed, which has the advantage of giving areas proportional to the corresponding spherical areas, an arrangement